Logic Matters

I have now had a chance to read the first part of Greg Restall and Shawn Sandefer’s Logical Methods, some 113 pages on propositional logic.

I enjoyed this well enough but I am, to be frank, a bit puzzled about the intended readership. The book’s Preface starts “Welcome to Logical Methods, an introduction to logic for philosophy students …”. And the text does indeed seem to start right from scratch. But Restall’s web-page for the book says “The text was developed through years of teaching intermediate (second-year) logic at the University of Melbourne.” While their Amazon blurb says “suitable for undergraduate courses and above.” Which suggests a rather unstable focus. And indeed, a significant amount of the material here, as we’ll see in a moment, is at what strikes me as a decidedly non-introductory level.

Certainly, things that can (and often should!) give pause to a philosophy student encountering formal logic for the first time are often skated over at speed. For example, when we do propositional logic, just what is the relation between the formal systems and our everyday inferences using the ordinary-language connectives? So, exactly what are these dratted “p”s and “q”s doing? On p.8 we are told that “declarative sentences express propositions”, and that we are going to be looking at propositional languages “where there are declarative sentences”. But then are also immediately told that our formal language is just designed “to express the forms of propositions combined with [the connectives]” (my emphasis). So do the “p”s and “q”s get interpretations as expressing propositions or not?

On p. 9 we are baldly told that “disjunctions will always be inclusive in this text” without a moment’s discussion of how things might or might not stand in ordinary language. And later, the much more vexed question of how the logician’s conditional might be related to the ordinary language conditional is relegated to a “challenge question” on p. 32. I wonder: if we don’t say rather more about the ordinary-language logical apparatus, how do we rack up a persuasive score sheet of the costs and benefits of various alternative formal choices? (Teachers using this book with real beginners might well be adding quite a bit of appropriate classroom chat on such matters as they go along — but I’m thinking here of a student reader taking the book “neat”.)

Again, the beginning reader is given just one worked example of a truth-table test for validity in action. And nothing is said e.g. about standard heuristics to speed things up (as in “you don’t need to work further on a line where the conclusion is true because that can’t give us a counterexample”) Yes, yes, of course truth-table testing complicated examples is as boring as heck. But surely(?) we do want our beginning students to be just a bit more au fait with how things can work out in practice.

So already, I’m not sure how well this is going to work with real beginners. But there are more serious worries. Restall and Sandefer advertise their book as presenting “proof construction on equal footing with model building” — but in fact that briskness over truth-tables is just one sign that their presentation is really skewed to emphasize proof-theoretic ideas. And so, long before we ever hear about the classical truth-functional interpretation of the connectives, we are tangling with why we might want detour-free proofs in a Gentzen-style natural deduction system. (By the way, much as though I like the elegance of Gentzen trees, I’m yet to be really persuaded that they trump Fitch-style proofs for introducing ND to students.)

And now, not only is the — I agree! — reasonably intuitive idea of a detour-free proof canvassed, but we actually get a full-on, ten-page, proof of normalizability for intuitionistic propositional logic (starting as early as p. 53 in the book). I honestly can’t imagine too many thinking that this is where they want their beginning philosophy students to be concentrating, so early in their logical encounters!

Now, I don’t want to carp, so let’s now recalibrate our expectations, and think of this as in fact a second-level text with some brisk reminders of the more elementary stuff. Then, on positive side, it can be said that the normalization proof and other parts of the discussion of Gentzen style ND are very accessibly done. So I can e.g. well foresee the relevant sections getting into the next edition of the Study Guide as warmly recommended reading on entry-level proof theory. But yes, for me at least, that is where this material really belongs, a step or two up from a first introductory text for philosophers. Call me old-fashioned!

I note that the text was typeset by the authors (and some of their aesthetic choices are a bit wonky!). But that does raise a question. I do wonder why, in 2023, since they have a nice PDF to hand, they have gone done the route of conventional publication when they could have got the book into so many more students’ hands by going down the free-PDF-plus-cheapo-print-on-demand route? Just saying.

I have hugely admired Jonathan Raban ever since I first read Old Glory forty years ago, and have praised his books here before. For example, I wrote this a few years ago (editing a little):

Now, how did that happen? Wanting to re-read Jonathan Raban’s Coasting, his evocation of a journey of discovery sailing round Britain, first published over thirty years ago, I just found a couple of days ago that our copy has disappeared from the shelves. A mystery:  I wonder what happened to it. So it is very good to discover that the book has recently been republished, along with four other books by Raban, by Eland, in rather handsomely produced paperbacks. I remember the book as being extraordinarily well written. The blurb on our new copy tells me that  Raban here “moves seamlessly between awkward memories of childhood as the son of a vicar, a vivid chronicle of the shape-shifting sea and incisive descriptions of the people and communities he encounters. As he faces his terror of racing water, eddies, offshore sandbars and ferries on a collision course, so he navigates the complex and turbulent waters of his own middle age. Coasting is a fearless attempt to discover the meaning of belonging and of his English homeland.” Which indeed is how I recall the book. I look forward to it!

I’ve been put in mind to read Coasting again because I have recently been re-reading with great  enjoyment two of Raban’s other books that are on our shelves (as it happens, another two of the five that have been republished by Eland). First there was For Love & Money, which is subtitled “Writing, Reading, Travelling: 1969–87”, and which reprints some early reviews and occasional pieces. The writing is consistently humane and insightful, but more than that, it is just so beautifully readable (the number of times I thought, “I wish I could write even half as well”). And then there was Raban’s early masterpiece, Old Glory from 1981, notionally recounting his voyage down the Mississippi in a small boat.

I say “notionally” as this complex work is lightly disguised as a straight travel book, a literal recounting of a journey taken. But the one-time English literature lecturer warns us clearly enough. One of the epigraphs of the book is from T. S. Eliot (writing of the  Mississippi), starting “I do not know much about gods; but I think that the river/Is a strong brown god …” The other epigraph is from Jean François Millet: “One man may paint a picture from a careful drawing made on the spot, and another may paint the same scene from memory, from a brief but strong impression; and the last may succeed better in giving the character, the physiognomy of the place, though all the details may be inexact.”

So we are set up for this to be a mythic tale (“the river/Is a strong brown god”)  and for the “Jonathan Raban” who features as the narrator and his adventures to be a very loose rendition of the author and his own journey (“all the details may be inexact”). And a mythic tale is indeed what we get, an ordeal by water, with auguries and signs, battles fought, even a princess won (but also lost, for this is a flawed epic, and the journey ends in emptiness as the river becomes the sea). But woven together with this are encounters with old American myths of frontiers and journeys. And, presciently — so striking, reading again now, nearly forty years later —  Raban notes the “deep, unsatisfied capacity for hero-worship” that makes many Americans long for a “strong” leader, a saviour. This is a many layered book, artful in the artlessness of its transparent prose. Wonderful.

And yes, I did indeed hugely enjoy re-reading Coasting. But Raban’s best book is surely Passage to Juneau (and this is saying something, for he is one of the very finest writers of non-fiction prose in English of recent decades). This is his 1999 book, notionally about sailing his 35ft ketch up the Inside Passage, from his home in Seattle to Juneau in Alaska. But like all great travel books, it is about so very much more — the voyage of Captain Vancouver that he is retracing, about the original Indian inhabitants and their relationship to the sea, about the idea of the sublime, about the death of his father, about his feelings for his young daughter, about other escapees he encounters at the edge of the world. And as ever “journeys hardly ever disclose their true meaning until after — and sometimes years after — they are over”. A masterpiece. Read it.

Jonathan Raban died a few days ago, aged 80. A stroke some years ago kept him confined to a wheelchair, an ironic fate, as the Guardian obituarist notes, for a writer who saw his journeys as “a means of escape, freedom and solitude, I could be happy … in a way I couldn’t be at home”. But he kept writing. And as another Guardian tribute tells us, “Raban’s memoir Father and Son is due to be published this autumn. … He is survived by his daughter, who said that on his last day he saw a bald eagle swooping and playing in the wind from his hospital window, before it flew off over Puget Sound, off Washington state.”